research-article

On the convergence of the Hegselmann-Krause system

Authors:

Arnab Bhattacharyya,

Mark Braverman,

Bernard Chazelle,

Huy L. NguyenAuthors Info & Claims

ITCS '13: Proceedings of the 4th conference on Innovations in Theoretical Computer Science

Pages 61 - 66

https://doi.org/10.1145/2422436.2422446

Published: 09 January 2013 Publication History

Abstract

We study convergence of the following discrete-time non-linear dynamical system: $n$ agents are located in R^d and at every time step, each moves synchronously to the average location of all agents within a unit distance of it. This popularly studied system was introduced by Krause to model the dynamics of opinion formation and is often referred to as the Hegselmann-Krause model. We prove the first polynomial time bound for the convergence of this system in arbitrary dimensions. This improves on the bound of n^O(n) resulting from a more general theorem of Chazelle [4]. Also, we show a quadratic lower bound and improve the upper bound for one-dimensional systems to O(n³).

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Cited By

Berenbrink PHoefer MKaaser DLenzner PRau MSchmand D(2024)Asynchronous opinion dynamics in social networksDistributed Computing10.1007/s00446-024-00467-3Online publication date: 26-Apr-2024
https://doi.org/10.1007/s00446-024-00467-3
Berenbrink PCooper CGava CMarzagão DMallmann-Trenn FRadzik TRivera NOshman RNolin AHalldorsson MBalliu A(2023)Distributed Averaging in Opinion DynamicsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594593(211-221)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594593
Srivastava TBernardo CAltafini CVasca F(2023)Analyzing the effects of confidence thresholds on opinion clustering in homogeneous Hegselmann–Krause models2023 31st Mediterranean Conference on Control and Automation (MED)10.1109/MED59994.2023.10185838(587-592)Online publication date: 26-Jun-2023
https://doi.org/10.1109/MED59994.2023.10185838
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Index Terms

On the convergence of the Hegselmann-Krause system
1. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

ITCS '13: Proceedings of the 4th conference on Innovations in Theoretical Computer Science

January 2013

594 pages

ISBN:9781450318594

DOI:10.1145/2422436

Program Chair:
Robert Kleinberg
Cornell University

Copyright © 2013 ACM.

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Published: 09 January 2013

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ITCS '13: Innovations in Theoretical Computer Science

January 9 - 12, 2013

California, Berkeley, USA

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Overall Acceptance Rate 172 of 513 submissions, 34%

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Cited By

Berenbrink PHoefer MKaaser DLenzner PRau MSchmand D(2024)Asynchronous opinion dynamics in social networksDistributed Computing10.1007/s00446-024-00467-3Online publication date: 26-Apr-2024
https://doi.org/10.1007/s00446-024-00467-3
Berenbrink PCooper CGava CMarzagão DMallmann-Trenn FRadzik TRivera NOshman RNolin AHalldorsson MBalliu A(2023)Distributed Averaging in Opinion DynamicsProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594593(211-221)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594593
Srivastava TBernardo CAltafini CVasca F(2023)Analyzing the effects of confidence thresholds on opinion clustering in homogeneous Hegselmann–Krause models2023 31st Mediterranean Conference on Control and Automation (MED)10.1109/MED59994.2023.10185838(587-592)Online publication date: 26-Jun-2023
https://doi.org/10.1109/MED59994.2023.10185838
Bechihi APanteley EDuhamel PBouttier A(2023)A Resource Allocation Algorithm for Formation Control of Connected VehiclesIEEE Control Systems Letters10.1109/LCSYS.2022.31878247(307-312)Online publication date: 2023
https://doi.org/10.1109/LCSYS.2022.3187824
Garg SShiragur KGordon DCharikar M(2023)Distributed algorithms from arboreal ants for the shortest path problemProceedings of the National Academy of Sciences10.1073/pnas.2207959120120:6Online publication date: 30-Jan-2023
https://doi.org/10.1073/pnas.2207959120
Continelli EPignotti C(2023)Consensus for Hegselmann–Krause type models with time variable time delaysMathematical Methods in the Applied Sciences10.1002/mma.959946:18(18916-18934)Online publication date: 2-Aug-2023
https://doi.org/10.1002/mma.9599
Li H(2022)Mixed Hegselmann-Krause Dynamics ⅡDiscrete and Continuous Dynamical Systems - B10.3934/dcdsb.2022200(0-0)Online publication date: 2022
https://doi.org/10.3934/dcdsb.2022200
Wang C(2022)Opinion Dynamics with Higher-Order Bounded ConfidenceEntropy10.3390/e2409130024:9(1300)Online publication date: 14-Sep-2022
https://doi.org/10.3390/e24091300
Parasnis RFranceschetti MTouri B(2022)On the Convergence Properties of Social Hegselmann–Krause DynamicsIEEE Transactions on Automatic Control10.1109/TAC.2021.305274867:2(589-604)Online publication date: Feb-2022
https://doi.org/10.1109/TAC.2021.3052748
De Pasquale GElena Valcher M(2022)Multi-dimensional extensions of the Hegselmann-Krause model2022 IEEE 61st Conference on Decision and Control (CDC)10.1109/CDC51059.2022.9992721(3525-3530)Online publication date: 6-Dec-2022
https://doi.org/10.1109/CDC51059.2022.9992721
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